Pith Number

pith:WR4V3OEM

pith:2007:WR4V3OEMXKFLX77YETF67YYKZ3

not attested not anchored not stored refs pending

Multiple Entropy Measures for Multipartite Quantum Entanglement

Dan Liu, Gui Lu Long, Xin Zhao

arxiv:0705.3904 v4 · 2007-05-26 · quant-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WR4V3OEMXKFLX77YETF67YYKZ3}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-04T15:02:21.410067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4795db88cba8abbfff824cbefe30aceef8a79f1d865e4639d0d4b98f769dede

Aliases

arxiv: 0705.3904 · arxiv_version: 0705.3904v4 · doi: 10.48550/arxiv.0705.3904 · pith_short_12: WR4V3OEMXKFL · pith_short_16: WR4V3OEMXKFLX77Y · pith_short_8: WR4V3OEM

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WR4V3OEMXKFLX77YETF67YYKZ3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b4795db88cba8abbfff824cbefe30aceef8a79f1d865e4639d0d4b98f769dede

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15cd12cc94a19917aa1a00f035c7ba9e2ecb685157d30e9005f0399e4dd02512",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2007-05-26T17:16:53Z",
    "title_canon_sha256": "5f44c03aa05782495645fbd6ac0008d26e5f55f1d052f7660c2dee895dcbde01"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0705.3904",
    "kind": "arxiv",
    "version": 4
  }
}